The present invention relates generally to medical imaging, and more particularly, to an efficient deformable registration methodology using a B-spline based free-form deformation model. The method utilizes sparse feature correspondences to estimate an elastic deformation field in a closed form. In a multi-resolution manner, the method is able to permit the recovery of small to large non-rigid deformations, such that the resulting deformation is globally smooth and guaranteeing one-to-one mapping between two images being registered.
Non-rigid (i.e., deformable) registration is an active and important topic of research in medical imaging. This process has numerous clinical applications, such as, for example, the study of PET-CT chest images and MR kidney perfusion time series, where respiratory motion causes gross changes in shape of the organs. It is employed in computational anatomy to adapt an anatomical template to individual anatomies. It is also used in brain imaging for spatial normalization of functional images, group analysis, and the like. Despite vast research efforts, however, non-rigid registration remains a primarily academic interest, and is not currently used in industry.
The reasons for the lack of industrial use are varied. State-of-the-art non-rigid registration methods are relatively slow, with running times on a typical workstation on the order of minutes to hours. Furthermore, most non-rigid registration methods do not directly solve the problem of anatomical correspondences. In many registration algorithms, maximum image similarities are pursued, and correspondences are only generated somewhat as a byproduct at the end of the registration. This poses problems when it comes to validation, since correct anatomical correspondences are the ultimate goal of a good registration method, as opposed to the ability and accuracy to transform one image into a clone of the other image. Finally, there is still no widely accepted validation protocol for measuring the quality of a deformation field generated by a registration method. For most available algorithms, no formal justification for the uniqueness of the solution is provided.
Existing methods for non-rigid registration fall into three general categories: feature-based registration, intensity-based registration, and hybrid methods that integrate the former. Feature based models utilize anatomical knowledge in determining sparse feature correspondences. These can be the faster of the implementations. The well-known disadvantage with this procedure is the need for user interaction to select good features for determining feature correspondences. Compared to rigid-registration, more features are necessary in non-rigid registration in order to recover a dense local deformation field, thus demanding a more automatic and principled method for extracting features, finding correspondences, and estimating elastic deformation. Intensity based methods are much more widely used in non-rigid registration. See, e.g., D. Rueckert, L. I. Sonda, C. Hayes, D. L. G. Hill, M. O. Leach, and D. J. Hawks, “Nonrigid Registration Using Free-Form Deformations: Application to Breast MR Images,” IEEE Transactions on Medical Imaging, Vol. 18, No. 8, pp. 712-721, August 1999. They can be fully automated without prior feature extraction. Typically a dense local deformation field is recovered by optimizing certain energy functions. A regularization term is usually included to explicitly force the smoothness of the deformation field. However, the intensity-based methods do not directly solve the anatomical correspondence problem. Another major concern with this method is that it tends to be very slow. By not discriminating good image elements (e.g., salient anatomical boundary features) from poor ones (e.g., noise, pixels/voxels in homogeneous regions that induce correspondence ambiguity), the cost functions to be optimized are often complex and non-convex, thereby making optimization prone to be stuck in local minima. Hybrid methods aim to integrate the merits of the feature-based and intensity-based models. See, e.g., D. Shen and C. Davatzikos, “Hammer: Hierarchical Attribute Matching Mechanism for Elastic Registration,” IEEE Transactions on Medical Imaging, Vol. 21, No. 11, pp. 1421-1439, November 2002; J. Kybic and M. Unser, “Fast Parametric Elastic Image Registration, IEEE Transactions on Image Processing [need cite]. These have been the subject of greater interest in recent times.
One important aspect of non-rigid registration is the choice of the local transformation (deformation) model. In the prior art, both parametric and non-parametric models have been considered. In parametric local deformation models, the thin-plate spline model and free form deformation model are most popular. In non-parametric models, elastic deformation and viscous fluid models are commonly employed.